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Eisenstein series on affine Kac-Moody groups over function fields


Authors: Kyu-Hwan Lee and Philip Lombardo
Journal: Trans. Amer. Math. Soc. 366 (2014), 2121-2165
MSC (2010): Primary 22E67; Secondary 11F70
DOI: https://doi.org/10.1090/S0002-9947-2013-06078-3
Published electronically: September 26, 2013
MathSciNet review: 3152725
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Abstract: In his pioneering work, H. Garland constructed Eisenstein series on affine Kac-Moody groups over the field of real numbers. He established the almost everywhere convergence of these series, obtained a formula for their constant terms, and proved a functional equation for the constant terms. In his subsequent paper, the convergence of the Eisenstein series was obtained. In this paper, we define Eisenstein series on affine Kac-Moody groups over global function fields using an adelic approach. In the course of proving the convergence of these Eisenstein series, we also calculate a formula for the constant terms and prove their convergence and functional equations.


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Additional Information

Kyu-Hwan Lee
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: khlee@math.uconn.edu

Philip Lombardo
Affiliation: Department of Mathematics and Computer Science, St. Joseph’s College, Patchogue, New York 11772
Email: plombardo@sjcny.edu

DOI: https://doi.org/10.1090/S0002-9947-2013-06078-3
Received by editor(s): February 8, 2011
Received by editor(s) in revised form: August 15, 2012
Published electronically: September 26, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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